Enumeration of Finite Rings with Jacobson Radical of Cube Zero

Details Enumeration of Finite Rings with Jacobson Radical of Cube Zero Enumeration of Finite Rings with Jacobson Radical of Cube Zero

1999-05-05

arxiv.org/abs/math/9905030v1

Mathematics

Rings and Algebras

22 pages

Scientific paper

In [1], finite associative rings wih identity and such that the set of all zero-divisors form and ideal M, called the Jacobson Radical, of cube zero and square non-zero, were constructed for all the characteristics. These rings are completely primary and we call them rings with property(T). In this paper, we associate with each ring with property(T) and characteristic p, invariants (integers) and determine (in certain cases) the number of isomorphism classes of these rings with given invariants.

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